{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "http://www.cs.ubc.ca/~nando/540-2013/lectures/gp.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import division\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\"\"\" This is code for simple GP regression. It assumes a zero mean GP Prior \"\"\"\n",
    "\n",
    "\n",
    "# This is the true unknown function we are trying to approximate\n",
    "f = lambda x: np.sin(0.9*x).flatten()\n",
    "#f = lambda x: (0.25*(x**2)).flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define the kernel\n",
    "def kernel(a, b):\n",
    "    \"\"\" GP squared exponential kernel \"\"\"\n",
    "    kernelParameter = 10\n",
    "    sqdist = np.sum(a**2,1).reshape(-1,1) + np.sum(b**2,1) - 2*np.dot(a, b.T)\n",
    "    return np.exp(-.5 * (1/kernelParameter) * sqdist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N = 10         # number of training points.\n",
    "n = 50         # number of test points.\n",
    "s = 0.05    # noise variance.\n",
    "\n",
    "# Sample some input points and noisy versions of the function evaluated at\n",
    "# these points. \n",
    "X = np.random.uniform(-5, 5, size=(N,1))\n",
    "y = f(X) + s*np.random.randn(N)\n",
    "\n",
    "K = kernel(X, X)\n",
    "L = np.linalg.cholesky(K + s*np.eye(N))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "_A = L.dot(np.matrix.getH(L))\n",
    "_B = K + s*np.eye(N)\n",
    "assert ((_A - _B) < 1e-12).all()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# points we're going to make predictions at.\n",
    "Xtest = np.linspace(-5, 5, n).reshape(-1,1)\n",
    "\n",
    "# compute the mean at our test points.\n",
    "Lk = np.linalg.solve(L, kernel(X, Xtest))\n",
    "mu = np.dot(Lk.T, np.linalg.solve(L, y))\n",
    "\n",
    "# compute the variance at our test points.\n",
    "K_ = kernel(Xtest, Xtest)\n",
    "s2 = np.diag(K_) - np.sum(Lk**2, axis=0)\n",
    "s = np.sqrt(s2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-5, 5, -3, 3]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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TTSxduhSAUaNGAVBeXs7XX3/NyJEjA+vY7XYAvvrqK9566y0Axo0bx0MPPXTC9rds2cKU\nKVPQ6bzyGR8ff0KZHTt28PPPPwfq4XA4GDhwIPv27aNbt2788Y9/DNRv9erVITnuqihhVygUzUOw\neahuu837CRFCiBq/+9P4ejwe4uLi2F3LTCDHr98YpJQMGTKE119/vdrvte0z1Cgfu0Kh6FAcPnw4\nkKXxtdde4/zzz6+2PCYmhm7durFp0ybAK8I//PADAOeddx5vvPEGABs2bKhx+0OGDGHVqlWBPO1F\nRUVA9fS/55xzDl999RW//vorABUVFezfv5+ePXty8OBBfvvtN4AThD9UKGFXKBQdilNOOYUVK1bQ\nq1cviouLuf32208os2HDBl544QXOOOMMTjvtNN59910AlixZwooVK+jduzdHjx6tcfuTJk2ic+fO\n9OnThzPOOIPXXnsNgNtuu42hQ4cyePBgkpKSWLduHTfeeCN9+vQJuGGMRiOrV69m2LBh9OvXj+Tk\n5GY5B01O2yuEyAReAVIACayWUi6pax2Vtleh6Hi0hbS9Bw8erDZpdXumKWl7Q+FjdwH3SSm/F0JE\nA7uEEP+SUv4cgm0rFAqFooE02RUjpcyRUn7v+98C7AXSm7pdhUKhaChdu3btENZ6Uwmpj10I0RU4\nE/g2lNtVKBTtg6a6dhVemnoeQybsQogo4C1gupSyrIbltwkhdgohdhYUFIRqtwqFoo1gNBoxm81K\n3JuIlBKz2YzRaGz0NkIy56kQQg98AHwipVxYX3nVeapQdDycTidZWVnYbLbWrkq7x2g0kpGRgV6v\nr/Z7i3WeCm80/wvA3mBEXaFQdEz0ej3dunVr7WooCI0r5jxgHHCxEGK373NlCLarUCgUikbQZItd\nSrkdaPoYXIVCoVCEhFYZeao6VxQKhaL5aBVhdzgcVFRUtMauFQqFosPTarli8vPzA6kyFQqFQhE6\nWk3YpZTk5OQEMqQpFAqFIjS0anZHj8dDbm6u8rkrFApFCGn1tL0Oh4P8/Hwl7gqFQhEiWl3YASor\nKykpKWntaigUCkWHoE0Iu5SSkpISFSmjUCgUIaBNCDt4xT0/Px+Hw9HaVVEoFIp2TZsRdvCKe3Z2\nNm63u7WrolAoFO2WNiXs4I2UycnJUZ2pCoVC0UjanLCDN/2nipRRKBSKxtEmhV1KSWVlJaWlpa1d\nFYVCoWh3tElhB6+4FxcXU1lZ2dpVUSgUinZFmxV28Ip7Xl6eipRRKBSKBtCmhR2O5ZRRkTIKhUIR\nHG1e2AHcbreKlFEoFIogaRfCDt5ImYKCAiXuCoVCUQ/tRtillFRUVKhIGYVCoaiHdiPscCxSRuWU\nUSgUitppV8IOx3LKqNmXFAqFombanbCDmn1JoVAo6qJdCjscyynj8XhauyoKhULRpmi3wg7gcrnI\ny8tTkTIKRW3Mnt3aNVC0Au1a2KWU2Gw2zGZza1dFoWibzJnT2jVQtALtWtjBK+4Wi4WysrLWropC\noVC0CXStXYFQIKXEbDaj0+mIiIho7eooFO0Kj8eD2+2u9gEQQlT7aDQahBDo9Xo0mnZvE3ZoOoSw\nw7GEYWlpaRgMhtaujkLR5nC73djtdmw2G1arFZfLhcfjQUqJEKLOdf3LpZRIKdFoNOh0OgwGA2Fh\nYYGPVqttiUNR1ENIhF0I8SIwHMiXUp4eim02Bn8YZHp6Onq9vrWqoVC0OlJKnE4nYUBubi42mw2P\nx4MQosZgg/oCEI5f7vF4cDgcOByOaqLvbzVHRkZiNBrrfWEomodQWezrgOXAKyHaXqPxh0Gmp6cr\n60FxUiGlxOFwUF5eTnl5OR6Ph25QbU6D5oggq7pNl8tFWVkZFosFAIPBQFRUFBEREeh0HcZB0OYJ\nyZmWUv5bCNE1+PKh2GvtuFyugLgri0HRkZFSYrfbA2Lud5U4nfDzzwZ2cj171sVQUKAlL09HQYGW\n/HwdpaUaYmI8xMe7iY93YzJ5fH/ddOrk4qyzbMTHN36MiF/sbTYbdrudwsJCjEYjsbGxREREqOey\nmRGheoP7hP2D2lwxQojbgNu8//frP2TIvxk8uJJBgypJTg59rnUhBOHh4aSkpKibSNHh8Hg8WCwW\nSkpK8Hg8eDySgwd1bN8ewfbt4ezYEU55+bEOTr1ekpjoJjnZRXKym9hYD2VlGoqLNRQXaykq0lJc\nrEHKY89Kz552zjnHxsCBVs4+20ZMTNMHA/o7YqOjo4mJiVEu0wYihNglpRxQb7mWEvaqJCScKcPC\nviM319tgOO00O4MGeUW+b187oepw999AiYmJodmgQtHKOBwOSktLKS8vx+2GbdvC2brVK+ZZWV6R\nzMx0csEFVs47z8oFd16K/bv3iYvz1Ptcud1QWqrh4EE9O3aE8803RnbtMmK3a9BoJKee6uDiiysZ\nNaqM1NSmG2NCCMLCwjCZTISHhysDLAjatLD37t1bvvPOu/zySxiffx7Otm0RfP+9EY9H0L27g4kT\nS/nLX8oxGJpeNyEEJpOJuLi4Jm9LoWgNpJRYrVaKi4txOByUlcH7d+3mhe19OUg3oinjEj7jMj7l\nMj6lB783eB/Fd99N8bRpJ/xut8Pu3UZ27Ajn66+9Qq/RwOWXVzBuXBlnnWWjqXoshECn0xEfH6/c\nNPXQ5oX93XffrfZbSYmGrVsjWLculp9+MpCQ4GL8+DLGji3DZGpaE1AIQUJCAjExMU3ajkLRkkgp\nqaysxGw243a7OXhQy8svx7J5czQVFRrOOsvKLbeUcvHFldTm0ejeowe///ZbyOp0+LCODRti2LQp\nmtJSLT172hk3royrrionIqJpWiKEQKvVkpCQoAS+FlpU2IUQrwODgEQgD5glpXyhtvJ9evaU73z4\nITW96qWEHTuMrFkTxxdfRBAe7uH66y389a+ldO7c+GyOQggSExOJjo5u9DYUipbAb6GbzWZcLhe7\ndoWxalUcn30WgU4Hw4aVM2FCKb171z/Je6iF3Y/VKnjvvSjWr49h714DMTFuxo8vY/LkEiXwzUiL\nW+wNYYBWK/99/vmYH38cZ7dutZb75Rc9L7wQx3vvReF2w5gxZdx7bzGxsY2z4IUQpKSkqNGpijaJ\nP/dRYWGhL7JLw9NPx/Pee9GYTG7GjPG2YFNSgvdvN5ewH6sz7Npl4KWXYvn44yhSUlw8+GARV11V\n3uS+Mr+LJikpCaPRGJoKt3PavLDv9HiQej0lEydScscdyMjIWsvn5mp5/vk4NmyIIS7Ow4wZZq69\ntrxRvj0hBKmpqYSHhzfhCBSK0GK32ykoKMDpdGK3S156KZbly024XHDrraVMmdI4S7i5hb0qu3YZ\nmDs3gT17jPTta+Oxx8z07dv0CXGEEERERJCQkHDSx8K3aWHv06uX3N67NzGbNgHgSk3FPGMGFcOH\n1+ie8fPTT2HMmpXIf/9rZMAAK3PmmOnZs/7m6PEIIVTqAUWbwOVyYTabqaysRErJF1+EM3duAgcO\nhHHppRXMnGlukguyJYUdwOOBf/wjigUL4iko0HHNNRYeeKAoZFE0cXFxxMXFnbTumTYt7P7OU8Pu\n3STMno1xzx4ASsePxzxrVp3rejyweXM08+fHU1amYfz4MqZNKyI6umHHIYQgPT2dsLCwRh+HQtFY\nPB4PpaWllJSUIKUkK0vH3LkJbNkSSdeuDh5/3MxFF1mbvJ+WFnY/5eWC55+P44UX4tBqJffdV8TN\nN5eFxD2j0WhITEw8Kf3vwQp7q6Zos/ftS/bbb1Pw1FO4EhIo/8tf6l1Ho4EbbrDwr38dYeRIC+vW\nxXDZZZls394w14qUkuzsbByOhlv8CkVjkVJSUVHBkSNHAqL+7rtRDBuWwddfh/Pgg2Y++igrJKLe\nmkRFSe6/v5hPPjnCOedYeeKJRG65JZW8vKal+ZBS4na7yc/PV9Nj1kGrWuzVKmK3I6u4RuLnz6fy\noouw/fnPdW7rhx8MPPRQEr/+qmfy5BKmTy+uNfSrJjQaDWlpacpyVzQ7DoeDgoICHA6Hbx4BwezZ\nibzzTjT9+9tYtCif9PTQClVQFrvDgdZsRtjtCN8k8Z64ONxxcRACd6WU8Prr0Tz5ZALh4ZKnnirg\nsssq618xCPzjVGJjY08K671duGJqI3z7djrdfDMAZTfcQNGMGXhiY2stb7UK5s5N4M03YzjzTBuL\nF+eTkRH8A6J87ormxOPxUFxcTFlZWSCHyg8/GJg+PZmsLB1TpxZzxx0lhLpfUFgsdOvbl7zly9Ed\nPoz+8GHv3yNHqBgyhKKZMwEw7NpF+g031Fz3yEiyN2zA0bs3ABFbt6I7dAjHKafg6NULj8kUdH1+\n+03PPfck89NPBkaNKuPRR81NDo2EY9EzycnJHf4ZbtfCjt1O3KpVmFauRDiduBITMc+aRcUVV9TZ\nufrBB5HMnJmEEJJ58woZOrQi6DoJIejUqZMKq1I0jtmza5xftLKykoKCgkDec48HVq+OZdGieJKT\nXSxalM+AAU2PHEFKtDk5uNPSAj9lDh6M/vDhGouXjRpF4VNPARC2bx+pEyciw8ICrWZNSQna4mKE\ny8XhLVtw+cKSk6dOJeqjjwLbcaWm4jjlFOy9emE76yysgwbVWU2HAxYvjmf16li6dnWycGE+ffqE\nxh0qhCAmJgaTydRhJwJp38LuQ/9//0fSI49g/P57ACqGDKHwiSdw15H75fBhHdOnJ/PDD0bGjClj\n5kwzRmNwx6jEXdFohKiWttTlclFYWIjVag1Y6fn5Wu69N5lvvgnnyivLeeKJwkaPyQDQ5uYSuWUL\nxm+/xbhrF7q8PA59+23g+UicORPjrl04u3TBlZmJs3NnnJ074+rcGWd6ev1uFikR5eXIiAjwpcCO\nfP99wnfsIGzfPsJ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vpI8YgXC7KZ46lZLbb2+R8QVVr3NMTAwRERGNfmm3pLAPBGZLKS/3\nfX8YQEr599rWaU/Cnvvcc6TefnvgtwM//si3e0xMmpRKYqKbV1/NJi2taQMX/ALv74DpKJZaS2Gz\n2SguLsZmszVaKLr36MFnS7Yw4bF+uCOj+XdOTyJenYMnOhrH6aeHtL7+6x0TE0N0dHS7SRkbapxO\nJxaLhbKysmphl02hastr1apY5s9P4PLLK1i8OI8waSd+4ULi1q4FwNa/P/kLF+LKyGjyfoPF/+IO\nDw8PtMwacv1bMldMOnCkyvcs32/HV+g2IcROIcTOoqKiEOy2ZagcPJii6dORvpOfPmIEF+i+Zt26\nHMxmLWPGpJGV1bQH0x9eVlRUxKFDhygqKmpXo9xaAyklFRUVZGVlkZOT0yC3y/GI8nKy6cRF0y7n\nUTmXN97I5g/8hm3gwJCKun/uzU6dOtG5c2dMJtNJK+oAer2e+Ph4unTpQlJSEnq9PqQtlsmTS3n0\n0UI++SSSu+5KwY6BoocfJueVV3ClpGDctYuMYcOIakEj0/8C80doHTlyhEOHDpGfn095eTkuV90t\nxGBpMdNQSrlaSjlASjkgPj6+pXbbdPR6SqZO5ehbbwEQduAAaTfcwJCPHuO1Nb9RWqph9Og0Dh5s\n+gPqv+glJSUcPnyY/Pz8dpmnojnxeDyUlpZWOz+NtvSkJPL990kZdDlp5KDBw4jLislID13uESFE\noMM8MzOT1NRUjEZjh3e5NAQhBFFRUWRkZJCamkp4eHjIzs8tt5Qxd24Bn30WyeTJqdhsAut553mT\nsV12GZrycpLvvZe4ZctCsr+GUHXMQHl5OQUFBRw+fJhDhw6RnZ0dGOhos9kabOiFwlw4CmRW+Z7h\n+63dU3z33YH//ZZb8ZQpxK1ZQ+xLL3FeQgIbNkxj/PhOjBmTxvr1OfToERpRkFJSXl5ORUVFoAMm\nKirqpHTT+HN2lJWVUVFREfitKYTt2+cdXPTttwD8QB80Lz1J5IWnNrm+oNxrjcE/H2l4eDhOp5OS\nkpKQZFgcM8aCXu/NxjlxYiqrV+cSaTKRt3Il0Rs3Ynr2WcqHDw/RUTQe/3G63W7cbjc2m63aADQh\nBBkZGZl1bcNPKHzsOrydp5fgFfTvgDFSyp9qW6e9+NiPx++/C9uzh7jnn6fg2WeRRiO//KJn/LhU\nEIJXXql9qr2mUNU3FxMTE1Krpq3icrkCPtiaBhUFQ32dpQUksoI7uYMVJFNYazk/9XWW+gesJCQk\nnBSdoc2Ny+WiqKio3uRsfuoKO3333SgeeCCJM86w8+KLOURH+1IsWK1If0y+lER89hmVF1/cLNFP\nTWXo0KHW/fv3R9RXLlThjlcCi/GGO74opXyyrvLtXdiPR1NWhmnUzdydN4v3xNW89FIOffo0nwvF\nLxbR0dFERkZ2qKa92+2msrISi8WC3ZfTPCSRE1JWG+4vr7ubf/6vG6+fMpOl6230H9Ct1klVgkEJ\nevPidDoxm81N6ksB+PjjSKZNS6ZnTwfr1uVgMlUPWY5+7TWSHnuMykGDyF+wAE8bcxsHK+wheSVJ\nKT+SUv5JStmjPlEP7NiXt6JqDgv/d///7eXhiNmwgdj9/+Pl0uvYYL+eGWPdQc+j2hj8vrmysjJy\nc3M5ePAgOTk5lJWVhazzpaXwu1mKiooCHUmFhYWBCJdQiLph1y7Srr2WsD17APjHP6I45Yd3WXfm\nAla+bj3h4W4IVVNGZGZmqrDVZkKv15Oamkp6enqTWqtDh1bw/PO57N+vZ+zYThQWVo8td6ek4I6N\nJeLzz8kYPhyjz1XX3miVkaf9+vWT27dv91bAd4H8Qu5Pcu/xeHC73YG//gRELpcLj8dTzffUUtTa\nzHO7iVm/nvhnn0VTWUmliOAp7WP0Wn0jAy9quegW//nT6XREREQE8oi0pcgLf4oFu92O1WoNxJw3\nx3XUHTlC/IIFRH34IQAVl1/OovPX8/jjiQwcaGXVqjwiIrz7rWsaxJrwW+jx8fFKzFsBm81GQUEB\nLperUffOV18ZmTw5lU6dXLzySg6dOh17TrXZ2aRMn45x1y6kRuONeb/zzjYxSUqLumIayoABA+TO\nnTsbvb7b7Q5knPMnI6oaPdJaaUa12dkkPPUUUf/8JwB76cX+B+bRe0po46CDpepLMywsLCD0BoMh\nqEx/TcXf4++/RlartUWuk7BYMK1cSey6dQiHA4/BQOnEiSyNfIjZCzozeHAFK1bkV5vKLlhh9xsg\n8fHxLZL0SVE7/lZrUVFRo+6lnTsNTJzYCZPJzfr1OWRmVmntulyYFi8m7vnnEVJiPecc8pYta3XX\nTLDC3nZMuQag1WoD2e2ifVnb/Jag1WqloqIitP7ZIHGnpZG/fDmWL7/E9Phseh3ey7RnIxiWHsmI\nERUtVg8/VfNs22y2QC+7/3etVoter6/20Wq11VxiVV1j/m35P/4OTY/HUy3Fq8PhqJbetWpdmhvj\njh2kTJ2K1jdWwnL11RTddz9L/nEqixbEc8UV5SxcmE99KTyqRkT5UXl+2hb+6xEVFYXZbA66g9XP\ngAF21q/PYcKEVEaP9ka1de/uC3zQ6Si+/35sAweSdO+9aEpKkBH16mmboV1a7MEgpcThcGC1WrFY\nLI1usjUaux3NR9sYtfEWvvvOyN//XsjNMZuxXnjhsR74NkZN1mdt56whZVsSbUEBmRdfjP3UUyma\nORNb7z7Mnx/P6tVxXHONhaefLqhxFHldrhchBJGRkcTHx7cpt5aiOo11z+zbF8b48alIKXjhhRMD\nH7QFBYjKSlxdugC+KJqwsFZxzXRoV0xjcDqdlJeXY7FYcLvdLSZCVqvg9ttTsH75E99xNq7UVIqn\nT8eiJjZuOlIS/tVXRL/5JvkLFwbmMNT//jvObt1wuQWPPJLEW29FM3ZsKbNnm2uNYKtJ2IUQGAwG\nEhMTQ56lT9E8NNY9c+CAjgkTOlFcrOW553I57zxbbTsgedo0tGYz+YsW4U5ODlHNg6NFo2LaA3q9\nHpPJROfOnUlPTycuLi7gdmhOwsMlq1blct65leyiH7rcXJJmzCBj2DDCt23zhuEpGozxu+/oNGYM\nnW6+maiPPqo2LNzZvTtWm4bbb0/hrbeimTatiDlzahf14/F3jKakpJCWlqZEvR3hd89kZGQQFhYW\n9PPdrZuLjRuzychwMmlSJz76qOY8+9q8PIzffkv4jh2kDx9O+FdfhbL6IeOkEfaqhIWFER8fT+fO\nnUlJScFgMDSrwBsMcNfLmSwbt4UbeY288C6E/d//0WnSJDqNHdtsk/B2RAw//EDqhAmkjR5N+H/+\ngzs2FvODD1Jx5ZWBMiUlGsaP78S2bRHMnVvA3XeXBD1jnRCCuLg4OnfuTEQ78qkqqqPX60lPT2/Q\ntJQpKW7eeCOHPn1s3H13Mhs2nDjrkjs1laMffID1nHPQmc2k3nwzpkWLoI3ldjophd2PPylTeno6\n6enpgSiH5hB5jQYem1VM5gOX0dn6C0u7zsMVG0f4t98S9c47Id9fRyTh8cdJv/ZaIr78Ek9UFEXT\npnH4iy8onTw50LGVna1l9Og0fvzRwPLl+YwZYwlq28V3301ERASZmZmYTCYV7dIB8EcvpaWlodPp\ngrqmMTEeXn45l4svruTxx5NYujTuhEa1OymJnFdeCXSwm5Yvp9O4cWjz8jAtWdIch9JgThofe7B4\nPB7KysoCkx03x/nZvDmKRx5J4qw/5vPW2XNw3joGd1oaAOH//je43VgHDWrxiZHbHE4nwm5HRkUB\nEP366yQ8+SSlN99M6aRJeEymasV//VXPzTd3orxcw6pVuZxzTi1+0ir43S7JyckYjcZmOQxF6yOl\npKioKJAiuD5cLgL9MzfdVMrjj5tr7BIzfv01yffcg66wkJKJE4l74YVmnftWdZ42EX8nTHFxcbMI\n/LZt4UydmkJSkpuXXsqha1cXeDxkXHEFYb/+ir1XL0omT/a6GE6yTlZRXk7Mxo3EvPQSFcOGUTRj\nhvd3ux1hteKJizthnZ07DUyenIpOJ3nppVxOPbX+lA5+i07NYnXyYLVayc3NDep5lhKefjqeNWvi\nuPTSChYuzCcy8sT1tIWFxC1bRtHDD9PttNPahLCf1K6YuvB3wnTp0oX4+PiQD+gZPNjKq6/mYLFo\nGDky3ZuCwOXCMnIkruRkDHv3kjJ9OpmXXELcypVo8/JCtu82iZSE7dlDwqxZdD7/fBKefBJ9djbG\n774LdDBLg6FGUd+8OYpx49KIjfWwaVN2vaLud8FlZmY2yAeraP+Eh4eTmZkZVO53IWDGjCJmzSpk\n69YIRo1KIzv7RCPLnZiIec4cpK/FJywWku6/H21OTrMcQzAoiz1IPB4PFosl5Bb877/rufXWFI4e\n1fO3vxVyww0WhN1O1NtvE7d6NfrDhwGQWi05GzZgO+uskOy3LWH8+msSnnwSw759gd+sZ51F6a23\nUjl4cK1Z9txumD8/nrVr4zj33EqWLcsnLq72vC9+t0tSUhLhbXQsgaJlkFJSWFgYdFrgf//b28I2\nGj08/3weZ55pr7Fc9x49KL3pJmJffRW3yUTB/PneTJEhQlnsIUaj0RAbG0vnzp2Ji4sLmZXXvbuT\nt9/O5pxzrDz8cBJz5iTg1Bqw3HgjR7ZsIefFFykfOhR3QgK2Pn0C60V+/DH6338PSR1aGmG3V2uB\nyIgIDPv24TaZKL3lFrI+/JCcN96g8pJLahV1i0Vw222prF0bx7hxpbz4Ym69om4ymcjMzFSirkAI\nQVJSEomJiUE9yxdeaGXz5qNEREjGjOnEe+/VHA4JUDx1KpUXXIC2uJjUW28lYe5csNf8ImgulMXe\nSPxT2YViIgDwdtbMnx/PCy/UbH0Kux1p8GaMFBYLXc45B43NhqNbNyovvpjKSy7B1r9/i0zO2xi0\nBQVEbNtGxNathH/1FfY+fcjZsAEA0+LF2M44A+u553pjQ+vh8GEdt92Wyu+/65k1q5CxY2uPfPFP\n3pCYmKhGjSpqxOFwkJOTE9QsRUVFGu68M4X//CecqVOLufvu4mq2R2Cgm8dD7Jo1xC9ciHC5sJ92\nGvlLluDs1q1JdVWdpy2Ew+HAbDY3aSLlqmzeHMVjjyWRmupi1apc/vSnEyft0ObmEv/MM0R89hna\nsrLA7+7YWCovuoiSu+9u8g0UCnRHjhD1zjtEbN2K8bhYfftpp5H9xhvIiIgG5T7fscPIXXel4PHA\n8uV5nHtuzZEv/jw3ycnJykJX1IvH4yEnJyeoqRYdDnjssSQ2b47myivLmTevINCpevy9bNi9m+Tp\n09EfOYInMpIjH38ciIBrDErYWxir1UphYWFIctJ8/72BO+5IwWrV8Oyz+Vx6aWXNBV0ujLt2EfHZ\nZ0Rs3UrYgQMAHP73v3Gle+cTj3n5ZTQVFdh798Z++uknhAiGBKeTsF9/xfC//+Ho0QP7AO8k6pHv\nv0/K9OkAeAwGrOee621dDBpU7eYORtg9HnjxxVgWLIinSxcnq1fneiOJasA/yCiULjNFx0dKSUFB\nQVDJxKSENWuO3Y9Ll+Zz6qmOmlNTWCwkPfoonqgoCp8MarqKWlHC3gr45yk1m81N7mDNydEyZUoq\nP/5oYNy4UmbMKMJorHt7+gMHMH73HZYbbgj8ljF0KGH/93+B786MDFyZmbhSUqi89FIqrrgCAFFZ\niS4vD6nReO9aX939sujMzAy4eaI3bMDw44/o8vLQ5uaiP3gQjc+HWDZ6dODm1R09StyKFVRecgnW\nc8+tNflZfcJeUKDlgQeS+PLLCIYMqWDBgvzAtGZVEUJgNBpJSkpSbhdFo5BSUlxcTGlpaVDP744d\nRu69N5niYi0PP2xm1pwkDtR0L0vp7e333Zdhe/Z4XTRnntmg+nXotL1tFSFEYLq64uLioAdD1ESn\nTm42bszmmWdMvPhiHDt2hLNwYX6doXzObt1OcMGU3H47hh9+wLBnD2E//4w+Kwt9VhYAroyMgLAb\nd+6k0y231LrtQ99+izsxEYC4NWvQHzlSfd+dO2Pv3Rvb2WcHfnOlp1P41FMNO/Dj2LYtnAcfTKai\nQjB3bgE33mg5YdyWP9olMTFRpQFQNAn/2Aa9Xk9hYWHg+a1t7tzuwGUkMIF1zJkznN38gxd6nEUC\nRXXuxx0Xh8ZioeTOOym+445AAruQHYey2JsPl8tFYWFhk+dp3L49nAceSKKkRMt99xXx17+WNm6e\nXZcL/cGD6HJz0ebl4TjlFByneycBifjsMxKeeKJ6eX8udSHI3rgRT0IC4LWwC/72N9ypqbhSUnBl\nZNQYXx4sNVnsdjvMn5/AunWxnHKKncWL82vsb/BHu6h4dEWoaehgpnXrYnj6iRgSUjUsXpzPWWfV\nMvLZbid+0SJi165FSIntjDPIf/ZZXEH0iylXTBuiqdN4gbc3fubMJD79NJJzz61kwYICUlNbJ/FQ\nQyd6buj2fv1Vz/Tpyezda2D8eK8bqupsR3AsR3pCQgLak2xkrqLlcDgcZGdn4/EENy9ucY+RXNt5\nB1lZOqZOLWbKlJJaJ3UxfvMNyQ88gC4nB094OOaZM7GMHl1nKhEVx96GMBqNZGRkkJSU1OgRrPHx\nHlauzOOppwr473+NDBuWwXvvRXaorL92u2DZsjiuvjqdvDwda9bkMmuWuZqo+6f5S0tLIzk5WYm6\nolkJCwsjIyMj6D6b/nzPe+9lMWJEOUuWxDN8eAZff11zDiLbwIFkffQRlquuQmO1kvTooyQ98EBI\n6q2EvYUQQhAVFdWkAU5CwKhRFt5//yhduji5554URo1KY8+e9p0vXAJbtkRw+eUZLF4cz+DBlXzw\nQRYXX3wsGkgIgU6nIzk5mfT0dAxBxLsrFKFAp9ORnp4etLhHR0sWLixg7docHA7BuHFpTJuWTF7e\niUaIJyaGgkWLyFu0CHd0NJUXXRSSOithb2E0Gk1gwo/GTobcrZuTTZuy+fvfCzh4UMdf/pLOQw8l\nUVDQ/qzXAwf0XMlHTJ6citEoeeWVbJYvzyclxetm8sejJyQkkJmZSWRkpPKlK1ocrVZLeno6+gZ0\ncg4ebOXjj7O4++5iPv00gssuy+TFF2Nx1RClW3HVVRzZupWKESMCv0V88gnawsJG1Vf52FsZp9NJ\nYWFhowc4WSyC5ctNvPxyLAaD5I47ipkwoTSYAZyNJlgfe22RBAAWoniCR1nEPYRjZTazuYvl6Kk5\nNh2AWbNg9uxG1lqhaDoej4fs7Gwcjpqj02p7Ng4e1PG3vyXyxRcRnHKKncceM3POObZa3en6X34h\n4+qr8URGYn78ccqvugqEUJ2n7Q273U5RUVGjBf7AAR3z5iWwZUsknTs7ufPOYkaMqDih0zEUNKXz\ntI8bJawAAAtnSURBVLBQw+uvx7B+fQxms47rrrOw4q0/UPHbN8CxSbJjYmIwmUxoGhX+o1A0H3WN\nUq3r2ZASPv00grlzE8nJ0XHGGTZuvbWUyy6rOCEztzY7m6RHHiHiyy8BqLjkEgrnzmXIzTcrYW+P\nNDVFwfbt4Tz1VDy//GLAZHIzalQZY8eWkZYWugiaxgj7L7/oeemlWN59NwqHQ8NFF1UydWoxZ55p\np3uPHhzwJTSLi4sjJiZGdYoq2jQej4fc3FxstuohjcE8G1ar4K23onnhhVgOH9bTubOTiRNLue46\nC+HhVZ55KYnevJn4J59Ea7HgjomhV0qKEvb2TFMEXkr45hsj69fHsmWL9x649NJKxo0rZeDA2pt/\nwRKssHs88MUX4bz4Yixffx2B0ejhuuss3HxzGT16eGPShRB0696d0pISoqOjlYWuaDdIKQPi7n9G\nG2L0uN3wr39FsmZNLLt3GzGZ3Nx0UxmjR5dVC2XW5uaS+OijeGJj6f/TT80v7EKIkcBsoBdwtpQy\nKLVWwh48DoeD0tJSysvLARos8tnZWl57LYY334yhqEjLH/7gYMiQCgYOtNGvn62ahVCXTzxYzMTz\nGZfwKZfxz6jryC43kZrqYvz4UkaNsgQyVvpHi5pMJqJjYuhQcZuKkwYpJTk5OdjtdqSUmJYsoXja\ntAZuA3btMrBmTRxbtnjTAZ96qp2LLqpk8OBK+va1o9VIhMPB5Vdf3SLC3gvwAKuA+5WwNx/+iT5K\nS0txu90NFni7XfDhh5G8+WY0u3cbcbkEYWGSvn1tnHOOjYEDrZxxhi2oTteqVkl5ueDnnw18+WU4\n27eHs2ePASkFMTFuzj3XytChFQwdWoFef8x/HhkZSUxMDAaDwfubEErYFe0Wv8/dHoKc6wcO6Pj0\n00i2bYvg+++NuN2CuDg3F17oFfmVKy9oOVeMEOJzlLC3CFJK7HY7JSUlVFZWIoRosMhXVAh27jTy\nzTfh7Nhh5KefDHg8Ap1OEh/vJj7ejcnkCfwfH+/GYJAUFOjIz9di+XAXh7qcS0GBlspKr+tEq5X0\n7WvnggsqOf98K7172wOp4YUQ6PV6YmNjiYyMPNHdooRd0c7xeDwcPXoUp/PEtBeNpbRUw5f/3979\nhch1l2Ecf56d2Z2dye4k5M/+SdPVBaMQalAaSqAXtSZotMHipaJSerEICi1USmLAXIggBFSwQgne\nCAZE0BCoFpOAKV5Yq9ZtoJqWIk3NrqJ2S7Lm7+7s68XM7EZJdmf3nJ0zOfP9wLA5mTNnX35Znv3l\nd855z2/KOneuopdeqmhmpqCdOz/YWcFue0LShCSNjY09ePHixcTft9vVajVdv35ds7Oziydx1vLv\neeVKj155pV+TkyW9+25BMzP113vv9WhmpqDLl+snMiuVBQ0NzWvs7d9q8LEHNTw8r23bahofn9Pe\nvdcXOy42f9kUi8XF2fmy1/8S7MiBWq2m6enpVMO9aWFBOn++pEOHHk0n2G2flTRyh7eORMSpxj7n\nxIw9UwsLC7px44ZmZ2d17drSHZtpPd3p1i2rUrn7CaLmMkt/f78GBgZULpdbb51LsCMnarWapqam\nNH+nu5BSkFrb3ojYn05JWE89PT2qVCqqVCqKCN26dUs3b97UjRs3dPPmTc3NzS2G72rDvliUisWl\n2XhToVBQX1+fSqWSKpXK0po50KUKhYK2b9+uqamplh61t17ox55DtlUqlVQqlVStViXVw3xubm4x\n5Ofn51Wr1VSr1bSwsLD4an6+2ays+bVQKKi3t3exR8v4+Hh6IX70aDrHATpAs7fMpUuXWu4KmXoN\nST5s+7OSvi9pm6Rf2J6MiE+mUhlS1eyK2He3HqJrOF5qaBOAnCkWi4sz9yzuFUp0N0hEnIyIHRFR\niohhQh0A6vr6+jQ6OprJ8iS3+QHAOunv79fw8HDbw51gx+qxJg60rFKpaMuWLW0Nd4Idq8eaOLAq\n1Wp1zQ/YWQuCHQDaYNOmTRoYGGhLuBPsANAGtrV161aVy+V1D3eCHQDaxLaGh4dTu+z4bgh2AGgj\n2xoZGWm95cYaEOwA0GaFQkGjo6Pr9mAZgh0AMtDb27tuNzAR7ACQkVKppKGhodTDnWAHgAxt2LBB\nmzdvTjXcCXYAyNjGjRs1ODiYWrgT7ADQAbZs2ZLaNe4EOwB0ANsaGhpa/jGSLSLYAaBD9PT0aHR0\nVIVCIdlxUqoHAJCC5jXuSZZkCHYA6DB9fX0aGRlZc7gT7ADQgcrl8pr7uBPsANChqtWqqtXqqsOd\nYAeADrZ582aVy+VVfYZgB4AO1rwMstHqN1r5DMEOAB2ueRnk9PT0Oy3tv94FAQCSKxQKunr16tVW\n9iXYASBnCHYAyBmCHQByhmAHgJxJFOy2j9m+YPu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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11031db00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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tM8Ldt+6vVvZAkYtG6frlg4T++Ef0Hg8V116D68wzh7XNe4sSdsWAEl+0iLYb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      "text/plain": [
       "<matplotlib.figure.Figure at 0x113ec8518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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p7aXtrbdofvY5XI2NmMePp3jKZDaVlJCcMIgp3VmIGgf+o2MInpGC0B/9Ij/3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\n/H8vqSWyQSvjVAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1140d3b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# PLOTS:\n",
    "plt.figure(1)\n",
    "plt.clf()\n",
    "plt.plot(X, y, 'r+', ms=20)\n",
    "plt.plot(Xtest, f(Xtest), 'b-', label='truth')\n",
    "plt.gca().fill_between(Xtest.flat, mu-3*s, mu+3*s, color=\"#dddddd\")\n",
    "plt.plot(Xtest, mu, 'r--', lw=2, label='predicted')\n",
    "plt.savefig('predictive.png', bbox_inches='tight')\n",
    "plt.title('Mean predictions plus 3 st.deviations')\n",
    "plt.axis([-5, 5, -3, 3])\n",
    "plt.legend()\n",
    "\n",
    "# draw samples from the prior at our test points.\n",
    "L = np.linalg.cholesky(K_ + 1e-6*np.eye(n))\n",
    "f_prior = np.dot(L, np.random.normal(size=(n,10)))\n",
    "plt.figure(2)\n",
    "plt.clf()\n",
    "plt.plot(Xtest, f_prior)\n",
    "plt.title('Ten samples from the GP prior')\n",
    "plt.axis([-5, 5, -3, 3])\n",
    "# plt.savefig('prior.png', bbox_inches='tight')\n",
    "\n",
    "# draw samples from the posterior at our test points.\n",
    "L = np.linalg.cholesky(K_ + 1e-6*np.eye(n) - np.dot(Lk.T, Lk))\n",
    "f_post = mu.reshape(-1,1) + np.dot(L, np.random.normal(size=(n,10)))\n",
    "plt.figure(3)\n",
    "plt.clf()\n",
    "plt.plot(Xtest, f_post)\n",
    "plt.title('Ten samples from the GP posterior')\n",
    "plt.axis([-5, 5, -3, 3])\n",
    "# plt.savefig('post.png', bbox_inches='tight')\n",
    "\n",
    "# plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "source": []
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  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
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